## IM Commentary

This problem assumes that students are familiar with the notation $x_0$ and $\Delta x$. However, the language "successive quotient" may be new. Examples in the third columns of the charts are designed to help students become familiar with this language. Depending on the students's prior exposure to exponential functions and their growth rates, instructors may wish to encourage students to repeat part (b) for a variety of exponential functions and step sizes before proceeding to the most general algebraic setting in part (c).

Two other problems (F-LE Equal Differences over Equal Intervals 1 and F-LE Equal Differences over Equal Intervals 2) illustrate the linear function portion of F-LE.1a.